Satellite X is in orbit around the Earth. An identical satellite Y is in a higher orbit. What is correct for the total energy and the kinetic energy of the satellite Y compared with satellite X?

The escape speed from a planet of radius R is v_esc. A satellite orbits the planet at a distance R from the surface of the planet. What is the orbital speed of the satellite?

A. $\frac{1}{2}{v}_{\text{esc}}$

B. $\frac{\sqrt{2}}{2}{v}_{\text{esc}}$

C. $\sqrt{2}{v}_{\text{esc}}$

D. $2v_{\text{esc}}$

A particle performs simple harmonic motion (shm). What is the phase difference between the displacement and the acceleration of the particle?

A. 0

B. $\frac{\pi }{2}$

C. $\pi$

D. $\frac{3\pi }{2}$

Two parallel plates are a distance apart with a potential difference between them. A point charge moves from the negatively charged plate to the positively charged plate. The charge gains kinetic energy W. The distance between the plates is doubled and the potential difference between them is halved. What is the kinetic energy gained by an identical charge moving between these plates?

A. $\frac{W}{2}$

B. W

C. 2W

D. 4W

An object at the end of a spring oscillates vertically with simple harmonic motion (shm). The graph shows the variation with time $t$ of the displacement $x$ of the object.

What is the velocity of the object?

A. $-\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

B. $\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

C. $-\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$

D. $\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$ 

A particle with a charge ne is accelerated through a potential difference V.

What is the magnitude of the work done on the particle?

A. $eV$

B. $neV$

C. $\frac{nV}{e}$

D. $\frac{eV}{n}$

The positions of stable nuclei are plotted by neutron number n and proton number p. The graph indicates a dotted line for which n = p. Which graph shows the line of stable nuclides and the shaded region where unstable nuclei emit beta minus (β^-) particles?

A circular coil of wire moves through a region of uniform magnetic field directed out of the page.

What is the direction of the induced conventional current in the coil for the marked positions?

An electron is fixed in position in a uniform electric field. What is the position for which the electrical potential energy of the electron is greatest?

A negative charge Q is to be moved within an electric field E, to equidistant points from its position, as shown.

Which path requires the most work done?

A satellite in a circular orbit around the Earth needs to reduce its orbital radius.

What is the work done by the satellite rocket engine and the change in kinetic energy resulting from this shift in orbital height?

The graph below shows the variation with time of the magnetic flux through a coil.

Which of the following gives three times for which the magnitude of the induced emf is a maximum?

A. 0, $\frac{T}{4}$, $\frac{T}{2}$

B. 0, $\frac{T}{2}$, T

C. 0, $\frac{T}{4}$, T

D. $\frac{T}{4}$, $\frac{T}{2}$, $\frac{3T}{4}$

A metallic surface is first irradiated with infrared radiation and photoelectrons are emitted from the surface. The infrared radiation is replaced by ultraviolet radiation of the same intensity.

What will be the change in the kinetic energy of the photoelectrons and the rate at which they are ejected?

Photons of a certain frequency incident on a metal surface cause the emission of electrons from the surface. The intensity of the light is constant and the frequency of photons is increased. What is the effect, if any, on the number of emitted electrons and the energy of emitted electrons?

Three possible features of an atomic model are

I. orbital radius

II. quantized energy

III. quantized angular momentum.

Which of these are features of the Bohr model for hydrogen?

A. I and II only

B. I and III only

C. II and III only

D. I, II, and III

The half-life of a radioactive nuclide is 8.0 s. The initial activity of a pure sample of the nuclide is 10 000 Bq. What is the approximate activity of the sample after 4.0 s?

A. 2500 Bq

B. 5000 Bq

C. 7100 Bq

D. 7500 Bq

Photons of discrete energy are emitted during gamma decay. This is evidence for

A. atomic energy levels.

B. nuclear energy levels.

C. pair annihilation.

D. quantum tunneling.

An object undergoes simple harmonic motion (shm) of amplitude $x$₀. When the displacement of the object is $\frac{x_0}{3}$, the speed of the object is $v$. What is the speed when the displacement is $x$₀?

A. 0

B. $\frac{v}{3}$

C. $\frac{\sqrt{2}}{3}v$

D. $3v$

Light of frequency 500 THz is incident on a single slit and forms a diffraction pattern. The first diffraction minimum forms at an angle of 2.4 x 10^–3 rad to the central maximum. The frequency of the light is now changed to 750 THz. What is the angle between the first diffraction minimum and the central maximum?

A.  1.6 × 10^–3 rad

B.  1.8 × 10^–3 rad

C.  2.4 × 10^–3 rad

D.  3.6 × 10^–3 rad

Light of wavelength λ is normally incident on a diffraction grating of spacing 3λ. What is the angle between the two second-order maxima?

A.  ${\sin }^{-1}\frac{2}{3}$

B.  ${\sin }^{-1}\frac{4}{3}$

C.  $2{\sin }^{-1}\frac{2}{3}$

D.  >90° so no second orders appear

Sea waves move towards a beach at a constant speed of 2.0 m s^–1. They arrive at the beach with a frequency of 0.10 Hz. A girl on a surfboard is moving in the sea at right angles to the wave fronts. She observes that the surfboard crosses the wave fronts with a frequency of 0.40 Hz.

What is the speed of the surfboard and what is the direction of motion of the surfboard relative to the beach?

The gravitational potential is $V$ at a distance $R$ above the surface of a spherical planet of radius $R$ and uniform density. What is the gravitational potential a distance $2R$ above the surface of the planet?

A. $\frac{V}{4}$

B. $\frac{4V}{9}$

C. $\frac{V}{2}$

D. $\frac{2V}{3}$

X and Y are two plane coils parallel to each other that have a common axis. There is a constant direct current in Y.

X is first moved towards Y and later is moved away from Y. What, as X moves, is the direction of the current in X relative to that in Y?

A coil is rotated in a uniform magnetic field. An alternating emf is induced in the coil. What is a possible phase relationship between the magnetic flux through the coil and the induced emf in the coil when the variations of both quantities are plotted with time?

Three observations of the behaviour of electrons are

I.   electron emission as a result of the photoelectric effect
II.  electron diffraction as an electron interacts with an atom
III. emission of radio waves as a result of electrons oscillating in a conductor.

Which observations are evidence that the electron behaves as a particle?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A pure sample of a radioactive nuclide contains N₀ atoms at time t = 0. At time t, there are N atoms of the nuclide remaining in the sample. The half-life of the nuclide is $t_{\frac{1}{2}}$.

What is the decay rate of this sample proportional to?

A.  N

B.  N₀ – N

C.  t

D.  $t_{\frac{1}{2}}$

A travelling wave has a frequency of $500 \mathrm{Hz}$. The closest distance between two points on the wave that have a phase difference of $60°\left(\frac{\mathrm{\pi }}{3}\mathrm{rad}\right)$ is $0.050 \mathrm{m}$. What is the speed of the wave?

A.  $25 \mathrm{m} {\mathrm{s}}^{-1}$

B.  $75 \mathrm{m} {\mathrm{s}}^{-1}$

C.  $150 \mathrm{m} {\mathrm{s}}^{-1}$

D.  $300 \mathrm{m} {\mathrm{s}}^{-1}$

White light is incident normally on separate diffraction gratings X and Y. Y has a greater number of lines per metre than X. Three statements about differences between X and Y are

I.  adjacent slits in the gratings are further apart for X than for Y
II.  the angle between red and blue light in a spectral order is greater in X than in Y
III.  the total number of visible orders is greater for X than for Y.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Two satellites W and X have the same mass. They have circular orbits around the same planet. W is closer to the surface than X. What quantity is smaller for W than for X?

A.  Gravitational force from the planet

B.  Angular velocity

C.  Orbital speed

D.  Orbital period

P and S are two points on a gravitational equipotential surface around a planet. Q and R are two points on a different gravitational equipotential surface at a greater distance from the planet.

The greatest work done by the gravitational force is when moving a mass from

A.  P to S.

B.  Q to R.

C.  R to P.

D.  S to R.

The graph shows the variation of electric field strength $E$ with distance $r$ from a point charge.

The shaded area X is the area under the graph between two separations $r_1$ and $r_2$ from the charge.

What is X?

A.  The electric field average between $r_1$ and $r_2$

B.  The electric potential difference between $r_1$ and $r_2$

C.  The work done in moving a charge from $r_1$ to $r_2$

D.  The work done in moving a charge from $r_2$ to $r_1$ 

A rectangular coil rotates at a constant angular velocity. At the instant shown, the plane of the coil is at right angles to the line $ZZ\mathit{\text{'}}$. A uniform magnetic field acts in the direction $ZZ\mathit{\text{'}}$.

What rotation of the coil about a specified axis will produce the graph of electromotive force (emf) $E$ against time $t$?

A.  Through $\frac{\mathrm{\pi }}{2}$ about $ZZ\mathit{\text{'}}$

B.  Through $\mathrm{\pi }$ about $YY\mathit{\text{'}}$

C.  Through $\frac{\mathrm{\pi }}{2}$ about $XX\mathit{\text{'}}$

D.  Through $\mathrm{\pi }$ about $XX\mathit{\text{'}}$

Monochromatic light is incident on a metal surface and electrons are released. The intensity of the incident light is increased. What changes, if any, occur to the rate of emission of electrons and to the kinetic energy of the emitted electrons?

The diameter of a nucleus of a particular nuclide X is $12 \mathrm{fm}$. What is the nucleon number of X?

A.  $5$

B.  $10$

C.  $125$

D.  $155$

A photon has a wavelength $\lambda$. What are the energy and momentum of the photon?

A sample of a pure radioactive nuclide initially contains $N_0$ atoms. The initial activity of the sample is $A_0$.

A second sample of the same nuclide initially contains $2N_0$ atoms.

What is the activity of the second sample after three half lives?

A.  $\frac{A_0}{2}$

B.  $\frac{A_0}{4}$

C.  $\frac{A_0}{6}$

D.  $\frac{A_0}{8}$

The diagram shows the diffraction pattern for light passing through a single slit.

What is

                                      $\frac{\text{wavelength of light}}{\text{width of slit}}$

A. 0.01

B. 0.02

C. 1

D. 2

A train is moving in a straight line away from a stationary observer when the train horn emits a sound of frequency $f_0$. The speed of the train is $0.10v$ where $v$ is the speed of sound. What is the frequency of the horn as heard by the observer?

A.  $\frac{0.9}{1}{f}_0$

B.  $\frac{1}{1.1}{f}_0$

C.  $\frac{1.1}{1}{f}_0$

D.  $\frac{1}{0.9}{f}_0$

Monochromatic light of wavelength $\lambda$ passes through a single-slit of width $b$ and produces a diffraction pattern on a screen. Which combination of changes to $b$ and $\lambda$ will cause the greatest decrease in the width of the central maximum?

A particle with charge −2.5 × 10⁻⁶ C moves from point X to point Y due to a uniform electrostatic field. The diagram shows some equipotential lines of the field.

What is correct about the motion of the particle from X to Y and the magnitude of the work done by the field on the particle?

The points X and Y are in a uniform electric field of strength $E$. The distance OX is $x$ and the distance OY is $y$.

What is the magnitude of the change in electric potential between X and Y?

A.  $Ex$

B.  $Ey$

C.  $E(x + y)$

D.  $E\sqrt{x^2 + y^2}$

Which is a correct unit for gravitational potential?

A. m²s⁻²

B. J kg

C. m s⁻²

D. N m⁻¹kg⁻¹

A planet has radius R. The escape speed from the surface of the planet is v. At what distance from the surface of the planet is the orbital speed 0.5v?

A. 0.5R

B. R

C. 2R

D. 4R

A satellite orbits planet $\text{X}$ with a speed $v_{\text{X}}$ at a distance $\text{r}$ from the centre of planet $\text{X}$. Another satellite orbits planet $\text{Y}$ at a speed of $v_{\text{y}}$ at a distance $\text{r}$ from the centre of planet $\text{Y}$. The mass of planet $\text{X}$ is $M$ and the mass of planet $\text{Y}$ is $4M$. What is the ratio of $\frac{v_{\text{X}}}{v_{\text{y}}}$?

A.  0.25

B.  0.5

C.  2.0

D.  4.0

A conducting ring encloses an area of 2.0 cm² and is perpendicular to a magnetic field of strength 5.0 mT. The direction of the magnetic field is reversed in a time 4.0 s. What is the average emf induced in the ring?

A. 0

B. 0.25 μV

C. 0.40 μV

D. 0.50 μV

The conservation of which quantity explains Lenz’s law?

A. Charge

B. Energy

C. Magnetic field

D. Mass

A magnet connected to a spring oscillates above a solenoid with a 240 turn coil as shown.

The graph below shows the variation with time $t$ of the emf across the solenoid with the period, $T$, of the system shown.

The spring is replaced with one that allows the magnet to oscillate with a higher frequency. Which graph shows the new variation with time $t$ of the current $I$ in the resistor for this new set-up?

Element X has a nucleon number $A_{\text{X}}$ and a nuclear density ${\rho }_{\text{X}}$. Element Y has a nucleon number of $2A_{\text{X}}$. What is an estimate of the nuclear density of element Y?

A.  $\frac{1}{2}{\rho }_{\text{X}}$

B.  ${\rho }_{\text{X}}$

C.  $2{\rho }_{\text{X}}$

D.  $8{\rho }_{\text{X}}$

In a photoelectric effect experiment, a beam of light is incident on a metallic surface W in a vacuum.

The graph shows how the current $I$ varies with the potential difference V when three different beams X, Y, and Z are incident on W at different times.

            I.   X and Y have the same frequency.
            II.  Y and Z have different intensity.
            III. Y and Z have the same frequency.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

What is true for the Bohr model for the hydrogen atom?

A.  Angular momentum of electrons is quantized.

B.  Electrons are described by wave functions.

C.  Electrons never exist in fixed orbitals.

D.  Electrons will continuously emit radiation.

The graphs show the variation with time of the activity and the number of remaining nuclei for a sample of a radioactive nuclide.

What is the decay constant of the nuclide?

A.  ${\text{0.7\hspace{0.05em}s}}^{-1}$

B.  ${\text{1\hspace{0.05em}s}}^{-1}$

C.  $\frac{1}{0.7}{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{1.5\hspace{0.05em}s}}^{-1}$

What was a reason to postulate the existence of neutrinos?

A. Nuclear energy levels had a continuous spectrum.

B. The photon emission spectrum only contained specific wavelengths.

C. Some particles were indistinguishable from their antiparticle.

D. The energy of emitted beta particles had a continuous spectrum.

A travelling wave on the surface of a lake has wavelength $\lambda$. Two points along the wave oscillate with the phase difference of $\mathrm{\pi }$. What is the smallest possible distance between these two points?

A.  $\frac{\lambda }{4}$

B.  $\frac{\lambda }{2}$

C.  $\lambda$

D.  $2\lambda$

When monochromatic light is incident on a single slit a diffraction pattern forms on a screen. The width of the slit is decreased.

What are the changes in the width and in the intensity of the central maximum of the diffraction pattern?

The diagram shows equipotential lines for an electric field. Which arrow represents the acceleration of an electron at point P?

Two charged parallel plates have electric potentials of 10 V and 20 V.

A particle with charge +2.0 μC is moved from the 10 V plate to the 20 V plate. What is the change in the electric potential energy of the particle?

A.  −20 μJ

B.  −10 μJ

C.  10 μJ

D.  20 μJ

A satellite of mass $m$ orbits a planet of mass $M$ in a circular orbit of radius $r$. What is the work that must be done on the satellite to increase its orbital radius to $2r$?

A.  $\frac{GMm}{r}$

B.  $\frac{GMm}{2r}$

C.  $\frac{GMm}{4r}$

D.  $\frac{GMm}{8r}$

A small magnet is released from rest to drop through a stationary horizontal conducting ring.

What is the variation with time of the emf induced in the ring?

In a photoelectric experiment a stopping voltage $V$ required to prevent photoelectrons from flowing across the photoelectric cell is measured for light of two frequencies $f_1$ and $f_2$. The results obtained are shown.

The ratio $\frac{V_2-V_1}{f_2-f_1}$ is an estimate of

A.  $e$

B.  $h$

C.  $\frac{e}{h}$

D.  $\frac{h}{e}$

Some of the nuclear energy levels of oxygen-14 (¹⁴O) and nitrogen-14 (¹⁴N) are shown.

A nucleus of ¹⁴O decays into a nucleus of ¹⁴N with the emission of a positron and a gamma ray. What is the maximum energy of the positron and the energy of the gamma ray?

The coil of a direct current electric motor is turning with a period T. At t = 0 the coil is in the position shown in the diagram. Assume the magnetic field is uniform across the coil.

Which graph shows the variation with time of the force exerted on section XY of the coil during one complete turn?

Three statements about Newton’s law of gravitation are:

I.   It can be used to predict the motion of a satellite.
II.  It explains why gravity exists.
III. It is used to derive the expression for gravitational potential energy.

Which combination of statements is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Three statements about radioactive decay are:

I.   The rate of decay is exponential.
II.  It is unaffected by temperature and pressure.
III. The decay of individual nuclei cannot be predicted.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Light of wavelength $\lambda$ is diffracted after passing through a very narrow single slit of width $x$. The intensity of the central maximum of the diffracted light is $I_0$. The slit width is doubled.

What is the intensity of central maximum and the angular position of the first minimum?

In two different experiments, white light is passed through a single slit and then is either refracted through a prism or diffracted with a diffraction grating. The prism produces a band of colours from M to N. The diffraction grating produces a first order spectrum P to Q.

What are the colours observed at M and P?

Two positive and two negative charges are located at the corners of a square as shown. Point X is the centre of the square. What is the value of the electric field E and the electric potential V at X due to the four charges?

The graph shows the variation with distance r of the electric potential V from a charge Q.

What is the electric field strength at distance s?

A.  The area under the graph between s and infinity

B.  The area under the graph between 0 and s

C.  The gradient of the tangent at s

D.  The negative of the gradient of the tangent at s

An object of mass $m$ is launched from the surface of the Earth. The Earth has a mass $M$ and radius $r$. The acceleration due to gravity at the surface of the Earth is $g$. What is the escape speed of the object from the surface of the Earth?

A.  $\sqrt{gr}$

B.  $\sqrt{2gr}$

C.  $\sqrt{2Mgr}$

D.  $\sqrt{2mgr}$

Three correct statements about the behaviour of electrons are:

I.   An electron beam is used to investigate the structure of crystals.
II.  An electron beam produces a pattern of fringes when sent through two narrow parallel slits.
III. Electromagnetic radiation ejects electrons from the surface of a metal. 

Which statements are explained using the wave-like properties of electrons?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Samples of two radioactive nuclides X and Y are held in a container. The number of particles of X is half the number of particles of Y. The half-life of X is twice the half-life of Y.

What is the initial value of $\frac{\text{activity of radioisotope X}}{\text{activity of radioisotope Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $1$

D.  $4$

Light with photons of energy 8.0 × 10⁻²⁰J are incident on a metal surface in a photoelectric experiment.

The work function of the metal surface is 4.8 × 10⁻²⁰J . What minimum voltage is required for the ammeter reading to fall to zero?

A.  0.2 V

B.  0.3 V

C.  0.5 V

D.  0.8 V

What is evidence for wave–particle duality?

A.  Line spectra of elements

B.  Electron-diffraction experiments

C.  Rutherford alpha-scattering experiments

D.  Gamma-ray spectra

The dashed line represents the variation with incident electromagnetic frequency $f$ of the kinetic energy E_K of the photoelectrons ejected from a metal surface. The metal surface is then replaced with one that requires less energy to remove an electron from the surface.

Which graph of the variation of E_K with $f$ will be observed?

The decay constant, $\lambda$, of a radioactive sample can be defined as

A.  the number of disintegrations in the radioactive sample.

B.  the number of disintegrations per unit time in the radioactive sample.

C.  the probability that a nucleus decays in the radioactive sample.

D.  the probability that a nucleus decays per unit time in the radioactive sample.

An electric field is established between two electrodes separated by distance d, held at a potential difference of V. A charged particle in this field experiences a force F.

What is the charge on the particle?

A.  $\frac{d}{FV}$

B.  $\frac{FV}{d}$

C.  $\frac{V}{Fd}$

D.  $\frac{Fd}{V}$

Two satellites are in circular orbits around the Earth. Both satellites have the same mass and satellite X is closer to Earth than satellite Y.

What is correct for the orbital periods of X and Y and the total energies of X and Y?

A resistor connects two parallel conducting rails a distance d apart. A conducting bar rolls along the rails at a constant velocity v through a uniform magnetic field of 2.0 T perpendicular to the rails as shown.

The voltage V across the resistor is measured.

The graph shows the variation of V with d.

What is v?

A.  0.33 m s⁻¹

B.  3.0 m s⁻¹

C.  6.0 m s⁻¹

D.  12.0 m s⁻¹

Two coils of wire are wound around an iron cylinder. One coil is connected in a circuit with a cell and a switch that is initially closed. The other coil is connected to an ammeter. The switch is opened at time t₀.

What is the ammeter reading before t₀ and what is the ammeter reading after t₀?

Monochromatic electromagnetic radiation ejects photoelectrons from a metal surface. The minimum frequency for which this is possible is $f$.

When radiation of frequency 2$f$ is incident on the surface, the kinetic energy of the photoelectrons is K.

What is the kinetic energy of the photoelectrons when the frequency of the radiation is 4$f$?

A.  K

B.  2K

C.  3K

D.  4K

A student quotes three equations related to atomic and nuclear physics:

I.    $E=\frac{-13.6}{n^2}\text{eV}$

II.   $N=N_0{\text{e}}^{-\lambda t}$

III.  $mvr=\frac{nh}{2\mathrm{\pi }}$

Which equations refer to the Bohr model for hydrogen?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Which emission shows a continuous energy spectrum?

A.  Photons during energy transitions between atomic energy states

B.  Gamma photons from the nuclei of radioactive isotopes

C.  Beta particles from the nuclei of radioactive isotopes

D.  Alpha particles from the nuclei of radioactive isotopes

The nucleus of the isotope hydrogen-2 has a radius R and a density $\rho$.

What are the approximate radius and density of a nucleus of oxygen-16?

The intensity pattern of monochromatic light of wavelength λ, is projected onto a screen.

What combination produces this pattern?

A mass oscillating in simple harmonic motion on the end of a spring has an amplitude $x$₀ and a total energy E_T. The mass on the spring is doubled and made to oscillate with the same amplitude $x$₀.

What is the total energy of the oscillating system after the change?

A.  E_T

B.  $\sqrt{2}$E_T

C.  2E_T

D.  4E_T

What is the pattern observed when white light passes through a diffraction grating?

Source S produces sound waves of speed v and frequency $f$. S moves with constant velocity $\frac{v}{5}$ away from a stationary observer.

What is the frequency measured by the observer?

A.  $\frac{4}{5}f$

B.  $\frac{5}{6}f$

C.  $\frac{6}{5}f$

D.  $\frac{5}{4}f$

Monochromatic light is incident on a single slit to form a diffraction pattern on a screen. The width of the single slit is then halved.

What are the change in the width of the central maximum and the change in the maximum intensity of the pattern?

Two spheres have the same positive charge. A point M is midway between the two spheres.

Along the line joining the spheres, what is true about the electrical field and the electric potential at M?

Two isolated point masses, P of mass m and Q of mass 2m, are separated by a distance 3d. X is a point a distance d from P and 2d from Q.

What is the net gravitational field strength at X and the net gravitational potential at X?

A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.

What is the magnitude of the electric field and direction of the electric field at the position of the particle?

The mass of Mars is about ten times that of the Moon. The radius of Mars is about twice that of the Moon.

What is the $\frac{\mathrm{escape} \mathrm{speed} \mathrm{from} \mathrm{Mars}}{\mathrm{Moon}}$?

A.  $\sqrt{5}$

B.  2$\sqrt{5}$

C.  5

D.  25

The escape speed from the surface of earth is v_esc. The radius of earth is R. A satellite of mass m is in orbit at a height $\frac{R}{4}$ above the surface of the Earth. What is the energy required to move the satellite to infinity?

A.  $\frac{\mathrm{m}{v^2}_{\mathrm{esc}}}{5}$

B.  $\frac{2\mathrm{m}{v^2}_{\mathrm{esc}}}{5}$

C.  $\mathrm{m}{v^2}_{\mathrm{esc}}$

D.  $2\mathrm{m}{v^2}_{\mathrm{esc}}$

A single loop of wire of resistance 10 Ω has its plane perpendicular to a changing magnetic field.

The graph shows the variation with time of the magnetic flux linked through the loop of wire.

What is the maximum current in the loop of wire?

A.  1.0 A

B.  2.0 A

C.  4.0 A

D.  20 A

Which law is equivalent to the law of conservation of energy?

A.  Coulomb’s law

B.  Ohm’s Law

C.  Newton’s first law

D.  Lenz’s law

Wire XY moves perpendicular to a magnetic field in the direction shown.

The graph shows the variation with time of the displacement of XY.

What is the graph of the electromotive force (emf) ε induced across XY?

Light of frequency $f$ is incident on a metallic surface of work function W. Photoelectrons with a maximum kinetic energy E_max are emitted. The frequency of the incident light is changed to 2$f$.

What is true about the maximum kinetic energy and the work function?

In the Bohr model for hydrogen, the radius of the electron orbit in the n = 2 state is four times that of the radius in the n = 1 state.

What is $\frac{\mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{electron} \mathrm{in} \mathrm{the} \mathrm{n} = 2 \mathrm{state}}{\mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{electron} \mathrm{in} \mathrm{the} \mathrm{n} =1 \mathrm{state}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  2

D.  4

What is the variation of nuclear density ρ with nucleon number A?

Which statement about atomic nuclei is correct?

The density is…

A.  directly proportional to mass number.

B.  inversely proportional to nuclear radius.

C.  inversely proportional to volume.

D.  constant for all nuclei.

Some energy levels for a hydrogen atom are shown.

diagram not to scale

What is the $\frac{\mathrm{wavelength} \mathrm{emitted} \mathrm{in} \mathrm{transition} \mathrm{X}}{\mathrm{wavelength} \mathrm{emitted} \mathrm{in} \mathrm{transition} \mathrm{Y}}$?

A.  $\frac{1}{2}$

B.  $\frac{27}{32}$

C.  $\frac{32}{27}$

D.  2

Radioactive nuclide X decays into a stable nuclide Y. The decay constant of X is λ. The variation with time t of number of nuclei of X and Y are shown on the same axes.

What is the expression for s?

A.  $\frac{\ln 2}{\lambda }$

B.  $\frac{1}{\lambda }$

C.  $\frac{\lambda }{\ln 2}$

D.  $\ln 2$

Two bodies collide on a horizontal frictionless surface. Body X, of mass 2.0 kg, moves with an initial speed of 0.80 m s^₋₁ and body Y is initially stationary. After the collision, body X moves at an angle of 90° to the initial direction of motion with a speed of 0.60 m s^₋₁.

What is the magnitude of the momentum of body Y after the collision?

A.  0.40 kg m s^₋₁

B.  1.0 kg m s^₋₁

C.  2.0 kg m s^₋₁

D.  2.8 kg m s^₋₁

Ball 1 collides with an initially stationary ball 2 of the same mass. After the collision, the balls move with speeds $v_1$ and $v_2$. Their velocities make angles ${\theta }_1$ and ${\theta }_2$ with the original direction of motion of ball 1.

What is $\frac{v_1}{v_2}$

A.  $\frac{\sin {\theta }_2}{\sin {\theta }_1}$

B.  $\frac{\sin {\theta }_1}{\sin {\theta }_2}$

C.  $\frac{\cos {\theta }_2}{\cos {\theta }_1}$

D.  $\frac{\cos {\theta }_1}{\cos {\theta }_2}$

Object X collides with object Y. Y is initially stationary. The tracks of the colliding particles after the collision are shown.

Which collision is elastic?

Diagram not to scale

A mass of 2.0 kg travelling at 5.0 m s⁻¹ collides with a mass of 4.0 kg travelling at 3.0 m s⁻¹. The masses collide at right angles. They join and move together after the collision at θ to the original direction of the 2.0 kg mass.

What is θ?

A.  34°

B.  37°

C.  50°

D.  56°

What are the fundamental SI units for angular impulse?

A.  kg m s⁻¹

B.  kg m² s⁻¹

C.  kg m s⁻²

D.  kg m² s⁻²

A flywheel of moment of inertia 0.50 kg m² rotates anti-clockwise with an initial angular velocity of 15 rad s⁻¹. A torque is applied to the flywheel and its angular velocity changes to 25 rad s⁻¹, rotating clockwise.

What is the angular impulse delivered to the flywheel?

A.  5.0 N m s

B.  10 N m s

C.  20 N m s

D.  40 N m s

A constant torque acts on a bicycle wheel. The wheel accelerates from rest to a final angular velocity of 16 rad s⁻¹ in a time of 4.0 s.

What is the angular displacement of the wheel during the acceleration?

A.  16 rad

B.  32 rad

C.  48 rad

D.  64 rad

Two objects of mass $M$ each are connected by a weightless rod of length $d$. A force $F$ is applied to each of the objects, at right angles to the rod as shown.

What is the torque acting on the system about the midpoint of the rod and what is the angular acceleration of the system?

A turntable of mass $M$ and radius $R$ spins freely about the vertical axis at an initial angular velocity $\omega$. The moment of inertia of the turntable about the axis of rotation is $\frac{1}{2}M{R}^2$. A small body of mass $m$ is dropped close to the edge of the turntable with a negligible initial velocity.

The body comes to rest relative to the turntable. What is the final angular velocity of the turntable?

A.  $\frac{M}{M+2m}\omega$

B.  $\frac{M}{M+m}\omega$

C.  $\frac{M}{2M+m}\omega$

D.  $\frac{2M}{M+m}\omega$

An object with a moment of inertia of 12 kg m² is rotating about its axis of rotation with an angular speed of 15 rad s⁻¹. A torque is applied to the object so that its angular speed increases to 50 rad s⁻¹.

What angular impulse acted on the object?

A.  420 kg m s⁻¹

B.  780 kg m s⁻¹

C.  390 kg m s⁻¹

D.  210 kg m s⁻¹

The graph shows the variation of torque with time acting on a rotating object.

What is the angular impulse acting on the object?

A.  The gradient of the line PQ

B.  The average gradient of the line PQR

C.  The area under the line PQ

D.  The area under the line PQR

The spacetime diagram shows coordinate axes of reference frames of Earth (x, ct) and of a spaceship (x', ct'). Three events P, Q and R are plotted.

Which statement is correct about the order of the events according to an observer on the spaceship?

A.  P and Q are simultaneous, R happens later.

B.  Q and R are simultaneous, P happens earlier.

C.  Q and R are simultaneous, P happens later.

D.  P and R are simultaneous, Q happens earlier.

Two spaceships, X and Y move in opposite directions away from a space station. The speeds of the spaceships relative to the space station are $u$ and $v$.

What is the speed of Y in the reference frame of X?

A.  $\frac{u-v}{1-{\displaystyle \frac{uv}{c^2}}}$

B.  $\frac{u-v}{1+{\displaystyle \frac{uv}{c^2}}}$

C.  $\frac{u+v}{1-{\displaystyle \frac{uv}{c^2}}}$

D.  $\frac{u+v}{1+{\displaystyle \frac{uv}{c^2}}}$

A spaceship is travelling at 0.60c from Earth when it launches a probe at 0.10c relative to the spaceship and away from Earth.

What is the speed of the probe relative to Earth?

A.  0.50c

B.  0.66c

C.  0.75c

D.  0.90c

The spacetime diagram shows an inertial reference frame S and a second inertial frame S’ that is moving relative to S.

The origins of the frames coincide when the clocks in both frames show zero.

Event $\text{X}$ is shown for the S reference frame.

Which event occurs at the same position in the S’ reference frame as $\text{X}$?

A spaceship leaves Earth and travels at a speed of 0.60c relative to the Earth to a point P.

P is 3.0 lightyears from Earth.

The spaceship then returns to Earth. Ignore the time taken to reverse the direction of the spaceship.

What is the time taken for the total journey to and from P as measured by an observer in the spaceship?  

A.  6.3 years

B.  5.0 years

C.  8.0 years

D.  10 years

A thermodynamic cycle consisting of an adiabatic, isovolumetric and isothermal processes is shown.

Which of the following correctly identifies the processes of the cycle?

An ideal gas expands isothermally. The work done by the gas is 100 J. What is the change in the internal energy of the gas?

A.  −100 J

B.  0

C.  +50 J

D.  +100 J

A thermodynamic process taking place in an isolated system is irreversible when the final state of the system has a:

A.  greater number of microstates than the initial state

B.  smaller number of microstates than the initial state

C.  greater internal energy than the initial state

D.  smaller internal energy than the initial state

Which statement is correct about the entropy of a non-isolated system?

A.  It always increases

B.  It always decreases

C.  It can only increase if the entropy of the surroundings decreases

D.  It can only decrease if the entropy of the surroundings increases

An energy of 200 J is transferred isothermally to an ideal gas. The temperature of the gas is 27 °C.

The entropy change of the gas is

A.  0.67 J K⁻¹

B.  0.14 J K⁻¹

C.  1.5 J K⁻¹

D.  7.4 J K⁻¹

Energy is transferred very slowly to ice of mass 0.050 kg at its melting point so that the ice melts completely. The melted water remains at 0 °C.

The specific latent heat of fusion of ice = 335 kJ kg⁻¹

What is the entropy change of the ice?

A.  0.041 kJ k⁻¹

B.  0.061 kJ k⁻¹

C.  0.041 J k⁻¹

D.  0.061 J k⁻¹

Three statements about the Carnot cycle are:

I.   The Carnot cycle is reversible.
II.  The net entropy change of the surroundings of the gas over one cycle is positive.
III. Heat transfer takes place in only two stages of the cycle  

Which statements are correct?

A.  I and II

B.  I and III

C.  II and III

D.  I, II and III

For a thermodynamic process, the entropy of the universe

A.  always increases during the process

B.  depends only on energy transferred during the process

C.  is zero during the process

D.  never decreases during the process

A space probe moves in a circular orbit around Earth. The kinetic energy of the probe is $E$.

The probe will reach the escape speed when its kinetic energy is increased at least to:

A.  $\sqrt{2}E$

B.  $2E$

C.  $2\sqrt{2}E$

D.  $4E$

What is the escape speed from the surface of a planet of radius $r$ that has an acceleration of gravity $g$ at its surface?

A.  $\sqrt{\frac{g}{r}}$

B.  $\sqrt{gr}$

C.  $\sqrt{\frac{2g}{r}}$

D.  $\sqrt{2gr}$

Which statement is correct about Compton scattering of a photon by an electron?

A.  The energy of the photon decreases.

B.  The wavelength of the photon decreases.

C.  The momentum of the photon is unchanged.

D.  The combined momentum of the particles increases.

A proton and an alpha particle are accelerated by the same electric potential difference. The kinetic energy of the proton is E and its de Broglie wavelength is λ. What is the kinetic energy and the de Broglie wavelength of the alpha particle?

An atom of hydrogen (${}_1{}^1\text{H}$) and an atom of helium (${}_2{}^4\text{He}$) are moving with the same kinetic energy.

The de Broglie wavelength of the hydrogen atom is ${\lambda }_{\text{H}}$ and the de Broglie wavelength of the helium atom is ${\lambda }_{\text{He}}$.

What is $\frac{{\lambda }_{\text{H}}}{{\lambda }_{\text{He}}}$?

A.  $\frac{1}{2}$

B.  $1$

C.  $2$

D.  $4$

An electron is accelerated from rest through a potential difference of 3.8 kV.

The de Broglie wavelength of the electron after acceleration is

A.  0.021 mm

B.  0.021 μm

C.  0.021 nm

D.  0.021 pm

The Compton effect can be explained using

A.  conservation of momentum

B.  kinematic equations applied in two dimensions

C.  the concept of a photon

D.  the wave theory of light

A beam of X-rays of wavelength 100.00 pm is scattered from a block of carbon. Radiation is observed at right angles to the incident beam.

What is the Compton shift for the observed radiation?

A.  0.1024 pm

B.  2.4322 pm

C.  2.4322 nm

D.  0.1024 nm

A car has an initial speed of 16 m s⁻¹. It decelerates at 4.0 m s⁻² until it stops.

What is the distance travelled by the car?

A.  4 m

B.  16 m

C.  32 m

D.  64 m

A block of mass 2.0 kg accelerates from a speed of 15 m s⁻¹ to a speed of 20 m s⁻¹ without changing its direction.

What impulse acts on the block?

A.  2.5 N s

B.  5.0 N s

C.  10 N s

D.  17.5 N s

A net force of 8.0 N accelerates a 4.0 kg body from rest to a speed of 5.0 m s⁻¹.

What is the work done by the force?

A.  50 J

B.  40 J

C.  32 J

D.  20 J

A disc of mass M and radius R is on a horizontal frictionless table. Two equal and opposite forces, each of magnitude F, act on the disc. The moment of inertia of the disc about its axis is $\frac{1}{2}M{R}^2$.

What is the angular acceleration of the disc?

A.  0

B.  $\frac{F}{MR}$

C.  $\frac{2F}{MR}$

D. $\frac{4F}{MR}$

A person stands in an elevator (lift). The total mass of the person and the elevator is 800 kg. The elevator accelerates upward at 2.0 m s⁻².

What is the tension in the cable?

A.  1.6 kN

B.  6.4 kN

C.  8.0 kN

D.  9.6 kN

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

A cylinder of mass $M$ and radius $R$ rotates at constant angular speed ω about an axis through its centre. The rotational kinetic energy of the cylinder is K.

The moment of inertia of the cylinder is $\frac{1}{2}M{R}^2$.

A second cylinder has mass $2M$, radius $2R$ and rotates with angular speed 2ω.

What is the rotational kinetic energy of the second cylinder?

A.  8K

B.  16K

C.  32K

D.  64K

A bird of weight $W$ sits on a thin rope at its midpoint. The rope is almost horizontal and has negligible mass.

The tension in the rope is

A.  less than $\frac{W}{2}$

B.  equal to $\frac{W}{2}$

C.  between $\frac{W}{2}$ and $W$

D.  greater than $W$

A spacecraft, moving with speed v relative to Earth, passes Earth on its way to a planet. As the spacecraft passes Earth, clocks on Earth and in the spacecraft show zero.

The planet is a distance D from Earth, according to an observer on Earth.

What are the readings on the Earth clock and on the spacecraft clock when the spacecraft arrives at the planet?

The internal energy of a real gas is

A.  zero.

B.  equal to the intermolecular potential energy of the particles.

C.  equal to the total kinetic energy of the particles.

D.  equal to the sum of the intermolecular potential energy and the total kinetic energy of the particles.

A gas undergoes one cycle of a cyclic process.

The net change in internal energy of the gas is

A.  zero.

B.  positive.

C.  negative.

D.  determined by the initial temperature of the gas.

A working refrigerator with the door open is placed in a sealed room.

The entropy of the room

A.  is zero.

B.  decreases.

C.  remains unchanged.

D.  increases.

The black-body radiation curve of an object at 600 K is shown. The intensity units are arbitrary.

What is the radiation curve of the same object at 450 K?

The original curve is shown with a dashed line.

Star X has a luminosity L and an apparent brightness b. Star X is at a distance $d$ from Earth.

Star Y has the same apparent brightness as X but is four times more luminous.

What is the distance of Star Y from Earth?

A.  $4d$

B.  $2d$

C.  $\frac{d}{2}$

D.  $\frac{d}{4}$

Four identical resistors, each of resistance $R$, are connected as shown.

What is the effective resistance between P and Q?

A.  $\frac{3R}{4}$

B.  $R$

C.  $\frac{4R}{3}$

D.  $4R$

Conductor X is connected to a cell of emf E. A power of 16 W is dissipated in X.

Conductor Y is made from the same material with the same diameter as X but is twice as long. A cell of emf 2E is connected to Y.

Both cells have negligible internal resistance.

What power is dissipated in Y?

A.  8.0 W

B.  16 W

C.  32 W

D.  64 W

Two containers, $\mathrm{X}$ and $\mathrm{Y}$, are filled with an ideal gas at the same pressure.

The volume of $\mathrm{X}$ is four times the volume of $\mathrm{Y}$. The temperature of $\mathrm{X}$ is 327 °C and the temperature of $\mathrm{Y}$ is 27 °C.

What is $\frac{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{X}}{\mathrm{amount} \mathrm{of} \mathrm{substance} \mathrm{in} \mathrm{Y}}$ ?

A.  $\frac{1}{8}$

B.  $\frac{1}{2}$

C.  $2$

D.  $8$

An electromagnetic wave has a wavelength that is about the size of the diameter of an atom.

What region of the electromagnetic spectrum does the wave belong to?

A.  Infrared

B.  Visible light

C.  Ultraviolet

D.  X-ray

A particle undergoes simple harmonic motion of period $T$. At time $t=0$ the particle is at its equilibrium position.

What is $t$ when the particle is at its greatest distance from the equilibrium position?

A.  $\frac{T}{8}$

B.  $\frac{T}{2}$

C.  $\frac{3T}{4}$

D.  $T$

Diagram 1 shows the variation with position of the displacement of a standing wave formed on a string.

Diagram 2 shows the variation with position of the displacement of a travelling wave moving to the right along a string.

Points P, Q, R and S are points on the string.

What is the phase difference between P and Q and the phase difference between R and S?

A mass of 0.25 kg hangs from a spring of spring constant 4.0 N m⁻¹.

What is the natural frequency of oscillation for this system?

A.  0.50 Hz

B.  0.64 Hz

C.  1.6 Hz

D.  2.0 Hz

Light from a monochromatic source is incident on a single slit and the resulting diffraction pattern is viewed on a screen. The graph shows the variation of intensity with distance on the screen.

The intensity of the source remains the same. The width of the slit is increased.

Which graph correctly shows the variation of intensity after the change? The original curve is shown with a dashed line.

Monochromatic light is incident on a diffraction grating. The diffraction pattern from the diffraction grating is then formed on a screen.

Only the central maximum and the first-order maxima can be observed on the screen.

What change will allow the second-order maxima to be observed on the screen?

A.  Decrease the distance between the diffraction grating and the source of light

B.  Increase the distance between the diffraction grating and the screen

C.  Increase the wavelength of the monochromatic light

D.  Reduce the number of lines per unit length of the diffraction grating

A solid metallic sphere is positively charged and isolated from all other charges.

The electric potential due to the sphere

A.  is constant inside the sphere.

B.  is constant outside the sphere.

C.  is smallest at the surface of the sphere.

D.  increases with distance from the sphere.

A planet orbits the Sun in an elliptical orbit moving in the direction shown.

At the position shown, which quantity is decreasing for the planet?

A.  Acceleration

B.  Angular momentum

C.  Kinetic energy

D.  Gravitational potential energy

Two long parallel wires P and Q are a distance d apart. They each carry a current.

A magnetic force per unit length $F$ acts on P due to Q.

The distance between the wires is increased to 2d and the current in Q is decreased to $\frac{I}{2}$.

What is the magnetic force per unit length that acts on P due to Q after the changes?

A.  $\frac{F}{8}$

B.  $\frac{F}{4}$

C.  $\frac{F}{2}$

D.  $F$

P is a point in a uniform electric field.

What is the direction in which the electric potential increases at P?

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

A rectangular conducting coil rotates at a constant angular velocity in a uniform magnetic field. The rotation axis of the coil is perpendicular to the field.

At one instant the plane of the coil is at an angle θ to the direction of the field.

The magnitude of the emf induced in the coil is

A.  never zero.

B.  at a maximum when θ = 0° or 180°.

C.  at a maximum when θ = 45° or 225°.

D.  at a maximum when θ = 90° or 270°.

A spherical planet has a radius R₀.

The graph shows the variation of the gravitational potential due to the planet with distance r from the centre of the planet.

What is the escape speed from the surface of the planet?

A.  1.6 × 10³ m s⁻¹

B.  2.2 × 10³ m s⁻¹

C.  3.2 × 10³ m s⁻¹

D.  4.5 × 10³ m s⁻¹

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A positive point charge of magnitude 1.0 μC and a point charge q are separated by a distance d.

An electron is placed at a distance d from the +1.0 μC charge. The electric force on the electron is zero.

What is q?

A.  −4.0 μC

B.  −2.0 μC

C.  2.0 μC

D.  4.0 μC

What is the sequence for the evolution of a main sequence star of about 2 solar masses?

A.  Red super giant → supernova → neutron star

B.  Red giant → planetary nebula → white dwarf

C.  Red giant → supernova → white dwarf

D.  Red super giant → planetary nebula → neutron star

The diagram shows the emission spectrum of an atom.

Which of the following atomic energy level models can produce this spectrum?

A photon of wavelength $\lambda$ scatters off an electron at rest. The scattered photon has wavelength $\lambda \text{'}$.

What is the fraction of the incident photon energy that gets transferred to the electron?

A.  $\frac{\lambda }{\lambda \text{'}}$

B.  $\frac{\lambda \text{'}}{\lambda }$

C.  $\frac{\lambda \text{'}-\lambda }{\lambda }$

D.  $\frac{\lambda \text{'}-\lambda }{\lambda \text{'}}$

Three statements about a nuclear fission reactor are:

I.   The heat exchanger transfers energy from the fuel rods to the moderator.
II.  The control rods must be good absorbers of neutrons.
III. The moderator must slow neutrons down.

Which statements about the reactor are correct?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II and III

The Hertzsprung–Russell diagram shows two stars, $\text{X}$ and $\text{Y}$.

What is $\frac{\mathrm{radius} \mathrm{of} \mathrm{X}}{\mathrm{radius} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  4

D.  16

The energy of the nth level of hydrogen is given by $-\frac{E_0}{n^2}$. What is the frequency of the photon emitted in the transition from $n=4$ to $n=2$?

A.  $\frac{1}{16}\times \frac{E_0}{h}$

B.  $\frac{3}{16}\times \frac{E_0}{h}$

C.  $\frac{1}{4}\times \frac{E_0}{h}$

D.  $\frac{3}{4}\times \frac{E_0}{h}$

Monochromatic light of frequency $f_1$ is incident on the surface of a metal. The stopping voltage for this light is $V_1$. When the frequency of the radiation is changed to $f_2$, the stopping voltage is $V_2$.

What is the quantity $\frac{V_2-V_1}{f_2-f_1}$ equal to?

A.  $h$

B.  $\frac{h}{e}$

C.  $\frac{h}{c}$

D.  $\frac{hc}{e}$

An alpha particle (${}_2{}^4\text{He}$) of initial energy 5.5 MeV moves towards the centre of a nucleus of gold‑197 (${}_{79}{}^{197}\text{Au}$).

What is the distance of closest approach of the alpha particle?

A.  1.0 × 10⁻¹³ m

B.  4.1 × 10⁻¹⁴ m

C.  2.1 × 10⁻¹⁴ m

D.  6.6 × 10⁻³³ m

The students vary V and measure the time T for the ball to move once from one plate to the other. The table shows some of the data.

V is provided by two identical power supplies connected in series. The potential difference of each of the power supplies is known with an uncertainty of 0.01 kV.

State the uncertainty in the potential difference V.

T is measured with an electronic stopwatch that measures to the nearest 0.1 s.

Describe how an uncertainty in T of less than 0.1 s can be achieved using this stopwatch.

Outline why it is unlikely that the relationship between T and V is linear.

Calculate the largest fractional uncertainty in T for these data.

The students suggest the following theoretical relationship between T and V:

$T=\frac{A}{V}$

where A is a constant.

To verify the relationship, the variation of T with $\frac{1}{V}$ is plotted.

Determine A by drawing the line of best fit.

State the units of A.

The theoretical relationship assumes that the ball is only affected by the electric force.

Suggest why, in order to test the relationship, the length of the string should be much greater than the distance between the plates.

The group obtains the following repeated readings for d for one value of W.

The group divides into two subgroups, A and B, to analyse the data.

Group A quotes the mean value of d as 2.93 cm.

Group B quotes the mean value of d as 2.8 cm.

Discuss the values that the groups have quoted.

The variation of d with W is shown.

Outline one experimental reason why the graph does not go through the origin.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of E are kg m⁻¹ s⁻².

Calculate $x$ and $y$.

The ruler has cross-sectional area A = a × b, where a = (28 ± 1) mm and b = (3.00 ± 0.05) mm.

Calculate the percentage uncertainty in the value of A.

Suggest an appropriate measuring instrument for determining b.

Calculate the average force exerted by the racquet on the ball.

Calculate the average power delivered to the ball during the impact.

Calculate the time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

Determine the speed of the tennis ball as it strikes the ground.

A student models the bounce of the tennis ball to predict the angle θ at which the ball leaves a surface of clay and a surface of grass.

The model assumes

• during contact with the surface the ball slides.
• the sliding time is the same for both surfaces.
• the sliding frictional force is greater for clay than grass.
• the normal reaction force is the same for both surfaces.

Predict for the student’s model, without calculation, whether θ is greater for a clay surface or for a grass surface.

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

Estimate, using the result from (a)(i), the nuclear radius of thorium-232 $\left({}_{90}^{232}\text{Th}\right)$.

Suggest one reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.

Outline why deviations from Rutherford scattering are observed when high-energy alpha particles are incident on nuclei.

The mass of a helium atom is 6.6 × 10^-27 kg. Estimate the average speed of the helium atoms in the container.

Show that the number of helium atoms in the container is 4 × 10²⁰.